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# 2.4 Solve Multi-Step Equations

2.4 Solve Multi-Step Equations. You will solve multi-step equations. How do you solve multi-step equations?. 30. 5 x. =. 5. 5. EXAMPLE 1. Solve an equation by combining like terms. Solve 8 x – 3 x – 10 = 20. 8 x – 3 x – 10 = 20. Write original equation. 5 x – 10 = 20.

## 2.4 Solve Multi-Step Equations

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1. 2.4 Solve Multi-Step Equations • You will solve multi-step equations. • How do you solve multi-step equations?

2. 30 5x = 5 5 EXAMPLE 1 Solve an equation by combining like terms Solve 8x – 3x – 10 = 20. 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – 10 + 10= 20 + 10 Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify.

3. SOLUTION When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally. EXAMPLE 2 Solve an equation using the distributive property Solve 7x +2(x + 6) = 39.

4. METHOD2 Do Some Steps Mentally = 9x 27 9 9 EXAMPLE 2 METHOD1 Show All Steps 7x + 2(x + 6) = 39 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 = 39 9x + 12 – 12= 39 – 12 9x = 27 9x = 27 x = 3 x =3

5. SOLUTION ANSWER In Step 2, the distributive property is used to simplify the left side of the equation. Because –4(x– 3) = –4x + 12, Step 2 should be 5x – 4x + 12 = 17. The correct answer is D. A B C D EXAMPLE 3 Standardized Test Practice

6. 1. 9d – 2d + 4 = 32 ANSWER 4 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

7. 2. 2w + 3(w + 4) = 27 ANSWER 3 EXAMPLE 2 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

8. 6x – 2(x – 5) = 46 3. ANSWER 9 EXAMPLE 2 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution.

9. 3 Solve . (3x + 5) = –24 2 (3x + 5) = –24 2 (3x + 5) = (–24) Multiply each side by , the reciprocal of. 3 3 2 3 2 3 2 2 3 3 2 EXAMPLE 4 Multiply by a reciprocal to solve an equation Write original equation. 3x + 5 = –16 Simplify. 3x = –21 Subtract 5 from each side. x = –7 Divide each side by 3.

10. 4. (z – 6) = 12 ANSWER 22 3 4 EXAMPLE 4 for Example 4 Multiply by a reciprocal to solve an equation GUIDED PRACTICE Solve the equation. Check your solution.

11. 5. (3r + 4) = 10 ANSWER 7 2 5 EXAMPLE 4 for Example 4 Multiply by a reciprocal to solve an equation GUIDED PRACTICE Solve the equation. Check your solution.

12. 6. – (4a – 1) = 28 ANSWER –8.5 4 5 EXAMPLE 4 for Example 4 Multiply by a reciprocal to solve an equation GUIDED PRACTICE Solve the equation. Check your solution.

13. SUMMER CAMP You are planning a scavenger hunt for 21 campers. You plan to have 5 teams. One camper from each team will be the recorder and the rest will be searchers. How many searchers will each team have? EXAMPLE 5 Write and solve an equation

14. SOLUTION Let sbe the number of searchers on a team. Then 1 + s is the total number of campers on each team. EXAMPLE 5 Write and solve an equation

15. ANSWER Because 4 searchers per team would require a total of 5(1 + 4) = 25 campers, 4 teams will have 3 searchers and 1 team will have 4 searchers. EXAMPLE 5 Write and solve an equation Write equation. 21 =5(1 + s) Distributive property 21 = 5 + 5s Subtract 5 from each side. 16 =5s 3.2 = s Divide each side by 5.

16. 7. WHAT IF? In Example 5, suppose you decide to use only 4 teams. How many searchers should there be on each team? ANSWER There will be 5 searchers on one team and 4 searchers on the other teams. EXAMPLE 5 for Example 5 Write and solve an equation GUIDED PRACTICE

17. ANSWER 2 ANSWER 11 ANSWER –4 Daily Homework Quiz Solve the equation. 1.8g–2+g=16 2.3b+2(b–4)=47 3. –6 + 4(2c+ 1) = –34

18. 4.(x – 6) = 12 Joe drove 405 miles in 7 hours. He drove at a rate of 55 miles per hour during the first part of the trip and 60 miles per hour during the second part. How many hours did he drive at a rate of 55 miles per hour? 5. 2 3 ANSWER 3 h ANSWER 24 Daily Homework Quiz

19. You will solve multi-step equations. • How do you solve multi-step equations? • To solve multi-step equations, first simplify one or both sides and then use inverse operations. • If a fraction is being multiplied by a quantity, use reciprocals to simplify instead of the distributive property. To solve a multi-step equation, first simplify and combine like terms. After simplifying, use inverse operations to isolate the variable.

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